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9-33.

Based on the given information, determine which pairs of lines, if any, are parallel. If none are necessarily parallel, write “none.”

Alternate interior angles and corresponding angles are equal only if the lines cut by the transversal are parallel.
Conversely, if the angles are equal the lines must be parallel.

  1.  

    These are alternate interior angles.

  2.  

    These are corresponding angles.

    and

  3.  

    In the diagram below, angles 1 and 12 are equal.
    Do any two lines look parallel?

    4 intersecting lines, first is horizontal on the bottom, second & third are each increasing, at different slants, fourth is decreasing, intersecting the second and third, top angle of the second & fourth line intersection is labeled 40 degrees, at the intersection of the third & horizontal lines, label right of third & above horizontal, is also labeled 40 degrees.

  4.  

    Vertical angles are always equal.

    and

  5. and are supplementary.

    Angle 6 would be supplementary to angle 7 if angle 7 was equal to angle 2.

Two increasing transversal lines, c, and d, cross two horizontal lines, e, and f, creating 4 points of intersection. The angles at each intersection are labeled, starting at the top left and going clockwise as follows: Intersection of c, and e: 1, 2, 6, and 5. Intersection of, d, and e: 3, 4, 8, and 7. Intersection of c, and f: 9, 10, 14, and 13. Intersection of, d, and f: 11, 12, 16, and 15.